Warm Up A man looks out from a water tower and waves to his daughter who stands on the ground, 60 feet from the base of the water tower. The angle of depression from the man’s position is 47°. How high is the water tower?

Answer 60 47° x x = 64.34

Law of Sines

So far, we’ve been working with right triangles So far, we’ve been working with right triangles! How do we find missing sides when we don’t have a right triangle?

The Law of Sines is a ratio that helps you look for a missing side or angle of any triangle. To use the Law of Sines, you must know the measurement of an angle and its opposite side, or “buddies!”

Example 1: Look for “buddies.” Solve ΔABC given that angle A = 36°, angle B = 48°, and a = 8. A = _____ B = _____ C = _____ a = _____ b = _____ c = _____

Example 2: Try it! Solve ΔABC given that angle A = 54°, angle B = 100°, and c = 18. A = _____ B = _____ C = _____ a = _____ b = _____ c = _____

Example 3: Use inverse trig. Solve ΔABC given that a = 6, b = 7, and angle A = 26.3°. A = _____ B = _____ C = _____ a = _____ b = _____ c = _____

Example 4: You try! Solve ΔABC given that a = 13, b = 8, and angle A = 38.8°. A = _____ B = _____ C = _____ a = _____ b = _____ c = _____

Example 5: Different letters! Solve ΔPQR given that q = 16, r = 21, and angle Q = 82.1°. P = _____ Q = _____ R = _____ p = _____ q = _____ r = _____